which is remarkable considering the extremely small forces
he measured,

roughly fifty one-millionth of the weight of the smaller of
his lead spheres.

Torsion balance

Cavendish acquired the torsion balance

of the man who invented it—geologist

John Michell, who also conceived the experiment

but died before beginning it.

The torsion balance let Cavendish measure the
force needed

to twist a wire or fiber

from which is hung a rotatable rod

with spherical weights balanced at its ends.

Cavendish built a wooden container for the
balance

to reduce the effects of heat or wind

and measured his results

using a pair of telescopes stuck through the
wood

focused on Vernier scales at the ends of the rod.

However, even inside the container, this torsion
balance

was never at rest, but occillated

with a period of about seven minutes;

therefore, Cavendish had to measure

the deflection due to the force of attraction

as the balance swung back and forth.

Sequence of results

Given the weight and dimensions of the torsion
balance,

the oscillation-period of the balance rod,

the distance between his roating and his fixed spheres,

the deflection of the torsion balance

(with tenths read from the secondary scale),

the weights of his spheres,

the radius of the earth,

one can solve a system of so many variables

given so many independent relations between them.

Otherwise, there is much we do not know.

Henry Cavendish is given credit for being the first to determine
the density of the earth, from which one may derive the
gravitational constant,
G
, which we use to express Newton’s law today:

F = G m1m2 / r2

where
F
is the force between two masses,
m1
and
m2
, separated by a distance
r
.

John Michell was elected a fellow of the Royal Society in
the same year as Cavendish, 1760. Cavendish rebuilt
Michell’s torsion balance and conducted the experiment, but
Michell was the scientist who realized that this device could
measure the extremely small forces of attraction between objects
smaller than mountains and, therefore, be used to determine the
force of gravity. Cavendish’s lead spheres were two inches
and twelve inches in diameter.

Michell’s genius was also shown in his work on
magnetism, explaining the causes of earthquakes and tsumanis, and,
in a letter to Cavendish that was not published until the
1970’s, explaining the effect of gravity on light and
existence and nature of dark holes.

Cavendish is also known for the discovery of hydrogen, for
his determination that the atmosphere is composed of one part
oxygen and four parts nitrogen (leaving only 1/120th of volume for
other gases), and numerous discoveries related to electricity that
were not known until a century after he died. But Cavendish
believed in phlogiston and his writings seem old-fashioned today;
his experiments preceded the naming of the elements that he
measured: hydrogen, oxygen, nitrogen, argon. Cavendish called
hydrogen ‘inflammable air’ and he called oxygen
‘dephlogisticated air.’